## Mathematics III

MA 2010      ENGINEERING  MATHEMATICS- III

Teaching Scheme

Examination Scheme

Lectures : 3 hrs/week

Mid-Sem – 30, Assignments, Quiz -20

End-Sem Exam- 50.

Unit 1

(10)

Linear Differential Equations & their applications : General Linear differential equations of order n, solution of linear differential equations with constant coefficients, method of variation of parameters, equations reducible to linear form (with constant coefficients), Cauchy’s & Legendre’s linear equations, simultaneous differential equations, application to electrical circuits

Unit 2

(08)

Partial Differential Equations & their Applications : Formation of partial differential equation, solution of partial differential equation of first order of the type f(x,y,z,p,q) = 0 (Introduction), one dimensional & two dimensional wave equations, problems related to radio- telephone & telegraphic equation, Laplace’s  equation in two dimensions with boundary conditions.

Unit 3

(12)

Vector Calculus : Differentiation  of vectors, gradient of a scalar point function, divergence & curl of a vector point function, vector identities, irrotational & solenoidal vectors, line integral, Green’s Lemma, Surface integral, Stoke’s theorem, Volume integral, Gauss Divergence theorem, applications to electromagnetic fields.

Unit 4

(08)

Laplace Transform : Definition, properties & theorems, Laplace transform of standard functions, unit step function, unit impulse function, inverse Laplace transform, application to solutions of linear differential equations(electric circuit problems)

Unit 5

(07)

Fourier Transform : Definition, fourier transform, fourier sine & cosine integrals, inverse fourier transform, applications of Fourier transform in sampling signals, discrete Fourier transform & it’s properties.

Unit 6

(07)

Z-Transform : Definition, properties of z-transform, z-transform of standard sequences, inverse  z-transform, relationship of z-transform with fourier transform, applications of z-transform to solutions of difference equations.

Text Books

·         A Text Book of  Applied Mathematics (Volume- III ), by P.N.Wartikar & J.N.Wartikar , Pune Vidyarthi Griha Prakashan, Pune.

·         Higher Engineering Mathematics, by B.S.Grewal, Khanna Publication, New Delhi.

Reference Books

# ·         Advanced Engineering Mathematics (7th Ed.) by Erwin Kreyszig, Wiley Eastern Ltd., Bombay.

·         Advanced Engineering Mathematics by C. R. Wylie, McGraw Hill Publications, New Delhi.

·         Advanced Engineering Mathematics ( 5th edition) by Peter V.O’Neil, Thomson Brook/cole, Singapore.